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handoflixue comments on Dutch Books and Decision Theory: An Introduction to a Long Conversation - Less Wrong
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It would seem that something is "Dutch Bookable" so long as the sum of probabilities doesn't add up to 1, which should not be a very difficult task at all.
I'm hoping this helps you clarify the question, since I feel like this answer probably doesn't actually address your intent :)
Well, depends on if the probabilities overlap. So:
P(A)=.5 P(A&B)=.1 P(&~B)=.2
is Dutch-Bookable
It seems closer to the solvability of a system of linear equations. Depends on what kind of probabilities you get? Like if you have
P(A), p(B), p(C), p(A&B)=P(B&C)=P(A&C)=0, it's trivial.
But if you have
P(<equation whose satisfiability is unclear>)=1/4
then you've got trouble.
Everyone's of course right. But it means I don't see a place for my train of thought to go.